I always find myself pissing myself whenever you post.
I'm naturally the nice guy, but, I can play the arrogant doucehbag. It is all about, as was just said, playing the game the they want it. Obviously, if you're looking for a long term type relationship, playing any games, and being who you are not is not a good strategy. As the old adage goes 'If she doesn't like you for you, she's not worth it.' But, if you are naturally a nice guy, then use that.
My story is pretty similar. This is my ex girlfriend who was, in the end, a... We won't go into that. But, the story.
I had the opposite situation to you, in that she was older than me, and had been at my workplace for a couple of years when I started there. Anyway, we got introduced on my first shift, and when I worked my next one, I tried to talk to her. Not because I wanted anything at that point, but, because I didn't really know anyone. Anyway, we spoke a bit, added her on facebook, and she went over to Japan a few weeks after I just started. I kept in contact with her while she was over there. And, we arranged to watch some TV and what not when she got back. Long story short, we ended up going out for over a year after that. Following that she destroyed me, and I now, can be a major douche.
I think, just talk to her whenever you get the chance, and just show an interest in her, listen to her etc. But, don't be someone your not just to try and get with her. That's a recipe for disaster.